Physics: transmission lines, infinite baffles & Quarter Waves

rwnano

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From stereo phile magazine on transmission line speakers.


Transmission Lines
In the October 1965 issue of Wireless World, Dr. Arthur Bailey made quite a technical splash with an article entitled "A Nonresonant Loudspeaker Enclosure Design." The article was not concerned with panel resonances, but rather with suppressing the delayed output and cabinet resonances produced by the woofer's back wave. Dr. Bailey concluded that the back wave must be absorbed to avoid these problems, and that the only safe way of doing this was to transmit the rearward energy down an infinite transmission line (TL), absorbing it so totally that it never reaches the listening room. Not having the resources for a line of such magnitude, he instead approximated the line with a damped and folded port about eight feet in total length. The optimum damping material he discovered experimentally to be long-fiber wool, packed at a density of 0.5 to 1.0 pounds per cubic foot. The use of damping material is crucial to the success of the TL enclosure, and represents the major departure from the previously known acoustic labyrinth, which used very little damping. The sound velocity through the wool is about 20% lower than it is in free air, so the stuffed line effectively increases the actual length of the line.

The wool also damps the inevitable pipe resonances. Yes, Virginia, every pipeline has a series of standing-wave resonances, so that even the TL enclosure is not truly "nonresonant." The TL length is generally chosen to correspond to the quarter-wavelength of the woofer's free-air resonant frequency. The old acoustic labyrinth was normally tuned to the woofer's half-wavelength at resonance—but then woofers in the '40s and early '50s had resonant frequencies around 50 to 60Hz, where a half-wavelength is only about 10 feet.



The port output for either a quarter- or half-wave line is in phase with the forward radiation of the woofer, so there's reinforcement of the lower octaves. However, with a quarter-wave line there's the added benefit of having the standing wave out of phase with the back wave of the cone, providing a kind of "braking" action that reduces cone excursion at the woofer's resonant frequency. The TL enclosure generally succeeds in its objective of suppressing back-wave energy and, with the right woofer, is capable of providing very clean and extended bass response. Internal pressures are low: compared with a closed box, there's not as much flexing or bending of the cabinet panels. But the fly in the ointment is that the long lines needed are expensive and complicated to build.
Incidentally, there's another way of achieving back wave suppression. With the infinite baffle enclosure, there is no delayed output because the back wave never encounters the back panel. Of course, no one has yet succeeded in building a truly infinite baffle, but a good approximation is to mount the woofer in the floor when there's a basement below, or to use the wall of the house as a baffle, radiating the back wave to the great outdoors. Why, none other than our own LA was recently contemplating the idea of using an empty water well (yes, he has one in his old house) as a baffle for a 12" Dynaudio woofer.
 
Your question, while succinct, is too big and it is bathed-in (loaded-with-) "jargon". Semantics, esp when they change over time, can cloud understanding.

"Transmission line" means very specific things to EE's...antenna people, etc. And to Bailey's original intent. To understand those, watch this old-school Bell Labs YT vid. BTW, those reflections at "impedance changes" happen in any horn or pipe with a sudden area change (like say a mouth termination, among others).

IB vs. acoustic suspension vs. just "sealed" are conventions. Nobody much knows them anymore, or at least uses them to differentiate as they used to. Here is one set of the old-school delineators.

QW loudspeakers just incorporate the axial standing wave either primarily or in addition to the customary compliance-inertance (acoustic C-L) modeling of a reflex cabinet. If one just looks at the first set of modes of a long pipe and a squattier box, it is evident that behavior differs.

These are all names & words...semantics. The loudspeaker names are like the dotted lines around "power supply" on a schematic. It's an abstraction that's convenient for us to use to talk about a certain facet of behavior. To focus on it, in-fact. If we are honest/intense, everything from the street power service through our device and involving whateverTF we call "ground" is power supply ("everything but the knobs" as my now RIP friend Al used to say). So it is with speakers.

Abe Cohen has the most wonderful exposition of the whole thing and I can't find that (2nd ed) book for free right now (except for borrowing). Start with a speaker in the air (dipole) hanging by nothing (4-pi space). Then add one infinite wall and mount the driver in it (2-pi). Now start bending the wall around until you have an open-back, etc...all of a sudden there's a different cavity resonance, etc. Now taper it expanding, now taper it contracting. Close it. Continue on, etc. It's all one big thing, it just takes time to visit all the regions and probe around until you realize it's all gray areas between jargon waypoints and that many actions are happening simultaneously in loudspeakers :) I think there are a lot of EE's around here laying in the weeds and that, esp antenna-people, they can explain relations/gray areas better. Hmmm. I do not know if this is "on the level" or not (?)
https://welib.org/md5/db782c62f6df624fa63a81e358868831 Striking-out. Maybe one day I can scan that bit of my hardcop

To get a grounding, I'd suggest a look at the old classics from hi-fi's "golden age" (1950's/60's). They were written for new readers and every one of them has some gem or other that's worth it. The gems are what the LLM's miss in their summaries (as well as the gestalt of the times). Cohen 1st ed. Briggs. Hartley. Badmaieff/Davis. Certainly Harry Olson's (more comprehensive if less-accessible). Eventually, examining the larger system happens and a decent tome for that is also from Davis.

So no--you're right--I didn't answer your questions. They're too big and to be honest, we all have different expectations regarding assistance. The simple answers only beget more questions (or should :) ) Hopefully you can find something of use. Now, everybody just models everything in either BEM or FEA or even FD flow code, depending on what they want. One can even run the original (16-bit) Akabak in wine / vbox+whatever to do quick investigations. Those are all case-specific, though. I think there are still those courses,too.

PS Nobody should be talking about Bailey's methods in 2026 except for historical admiration :)
 
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